"(Benim) cildimin ciddi bir sorunu var." = My skin has a serious condition /problem.
We would need genitive case ("-in") on "cildim" (my skin) because it is now the possessor of the problem. And possessive 3rd person suffix ("-u") on "sorun" because it now belongs to my skin (an "it") rather than to me. So, I agree with gidcowboy that it sounds a little more removed, especially if we omit "benim" as well.
I'm not a native speaker (just a grammar nerd), so I'm also open to correction :-)